Wich could be the reason the author had to write the text? Wich could be the reason that led the author to write this piece of text?

wich = I have never seen this word before.

which = This word does not have the same meaning in English as "qual" in Portuguese. It is used when the speaker has given at least two possible choices to the listener, and the speaker is asking the listener to make choice. Permit me to give some examples.

(a)

My name is Dale. What is your name?

Chamo-me Dale, Qual é seu nome?

(b)

My name is Dale. John, Robert, and Phillip. Which is your correct name?

Chamo-me Dale. John, Robert e Phillip. Qual é seu nome certo?

Do you see the difference? No choice was given in (a) before the question was asked. However, in (b) the listener was given three choices.

What do you want to drink?

I have Budweisser, Corona, Tecate, and Brahma. Which beer do you want to drink?*

What are you taking to the beach?

We have a ball, a basket, an ice chest, a blanket, and a radio. We can only take two. Which do you plan to take to the beach?*

*In colloquial American English, expect to hear both forms.

Which could be the reason the author had to write the text?

Which could be the reason that led the author to write this piece of text?

Both are correct IF the speaker has given us as listeners two or more possible reasons.

What could be the reason the author had to write the text?

Which could be the reason that led the author to write this piece of text?

Both are correct because no choice of reasons was given prior to posing the question.